材料科学基础
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson fifteen
§ 4.8 Twinning (I)
—— Macroscopic Aspect
? Ⅰ.
? Ⅱ.Rules governing the change in
length.
1,Change in shape of a hemisphere with unit radius.
before twinning:
bnlrlL ????? )( ???
? ?11z 222 ??? yx
? ?2zz ?????? yyxx
? ? ? ?1in t o2s u b s t it u t e
e l l i p s o i df o re q u a t i o n1z)( 222 ???????? zryx
2,Undistorted planes and directions.
?
?
?
??
??
.D.T
.P.T
1
1
?
K
?
?
?
?? p l a n es h e a ra n dofoni n t e r s e c t it h e 22
2
K
K
?
Twin elements —— K1,?1,K2,?2
K1 ?1 K2 ?2
FCC
BCC
HCP
)111(
)112(
)111(
)2110( )0121(
)211(
]211[
]111[
]0111[
]112[
]111[
]1110[
FCC
K1,?1 K2,?2
BCC
K1,?1
K2,?2
c
a1
a2
a3
HCP
)2110( ]0111[
)0121( ]1110[
3.
4,Rule for elongation or reduction of R.D,
All R.D,in the region where K1 and K2 makes an
obtuse (acute) angle will increase (reduce) its length
after twinning.
)2(c t g2 ?? ??? AA
C D
? Ⅲ.Application,take HCP for
example
Suppose:,)2110(1 ?K )0121(2 ?K
)86.1(c r y s t a l ?acZn
acc
a
/
3
2/
2/3tg ???
2?
?3a
c/2
)0121( c
a1
a2
a3
HCP
)2110( ]0111[
]1110[
a n g lea c u t e3?ac
a n g leo b t u s e3?ac
?862)86.1(Zn ??? ?
a
c
?9023W h e n ?? ?
a
c
C
I
II
III
IVVI
V
0112
0211
0110
0112
)2110(
)2101(
)1210(
)2011(
)0211(
)0121(
?2(I,II) (III,IV) (V,VI)
A － － －
B ＋ － －
C ＋ － ＋
D ＋ ＋ ＋
zone
21,KK
Examples and Discussions
Exercise
Thank you !
15